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Question: Calculate second electron affinity of oxygen of the process, \({O^ - }(g) + {e^ - }(g) \to {O^{2 -...

Calculate second electron affinity of oxygen of the process,
O−(g)+e−(g)→O2−(g){O^ - }(g) + {e^ - }(g) \to {O^{2 - }}(g)
By using the following data:
i.Heat of sublimation of Mg(s)=+147.7kJmol−1Mg(s) = + 147.7kJmo{l^{ - 1}}
ii.Ionisation energy of Mg(g)Mg(g) to form Mg2+(g)=+2189.0kJmol−1M{g^{2 + }}(g) = + 2189.0kJmo{l^{ - 1}}
iii.Bond dissociation energy for O2=+498.4kJmol−1{O_2} = + 498.4kJmo{l^{ - 1}}
iv.First electron affinity of O(g)=−141.0kJmol−1O(g) = - 141.0kJmo{l^{ - 1}}
v.Heat formation of MgO=−601.7kJmol−1MgO = - 601.7kJmo{l^{ - 1}}
vi.Lattice energy of MgO=−3791.0kJmol−1MgO = - 3791.0kJmo{l^{ - 1}}
A.235.6kJ/mol235.6kJ/mol
B.468.7kJ/mol468.7kJ/mol
C.544.4kJ/mol544.4kJ/mol
D.744.4kJ/mol744.4kJ/mol

Explanation

Solution

At first think about the elementary steps involved in the formation of magnesium oxide, so that you can get some idea about how to use the above given values in order to calculate the second electron affinity of oxygen.

Complete step by step answer:
In the question, we have given that
O−(g)+e−(g)→O2−(g){O^ - }(g) + {e^ - }(g) \to {O^{2 - }}(g)
The elementary steps used for the formation of magnesium oxide are given as,
Let’s take the second electron affinity of oxygen is qq
Mg(s)→Mg(g) Mg(g)→Mg2++2e− 12O2(g)→O(g) O(g)+e−→O−(g) O−(g)+e−→O2−(g) Mg2+(g)+O2−(g)→MgO(s)  Mg(s) \to Mg(g) \\\ Mg(g) \to M{g^{2 + }} + 2{e^ - } \\\ \dfrac{1}{2}{O_2}(g) \to O(g) \\\ O(g) + {e^ - } \to {O^ - }(g) \\\ {O^ - }(g) + {e^ - } \to {O^{2 - }}(g) \\\ M{g^{2 + }}(g) + {O^{2 - }}(g) \to MgO(s) \\\ ΔH(kJ/mol) 147.7 2189.0 498.4 \-141.0 q 3791.0  \Delta H(kJ/mol) \\\ 147.7 \\\ 2189.0 \\\ 498.4 \\\ \- 141.0 \\\ q \\\ 3791.0 \\\
ΔH1=−1346.1+q\Delta {H_1} = - 1346.1 + q
Mg(s)+12O2(g)→MgO(s)Mg(s) + \dfrac{1}{2}{O_2}(g) \to MgO(s)
ΔH2=−601.7\Delta {H_2} = - 601.7
We all know that the heat of formation of a substance through all elementary steps is equal to the heat of formation of a substance by direct equation.
Hence, the heat of formations in both process are equal
Then,
ΔH1=ΔH2\Delta {H_1} = \Delta {H_2}
1346.1+q=−601.7 q=744.4kJ/mol  1346.1 + q = - 601.7 \\\ q = 744.4kJ/mol \\\
The required second electron affinity of oxygen is 744.4kJ/mol744.4kJ/mol.
So the correct option is D.

Additional Information:- Electron affinity is defined as the minimum amount of energy released when an electron is added to its neutral atom or molecule in its gaseous state to form a negative ion. The first electron affinity of oxygen is negative and it is less than the electron affinity of the fluorine.

Note:
The second electron affinity of oxygen is positive because after adding two electrons to its neutral oxygen atom, it attains a noble gas configuration. A noble gas configuration being most stable, releases energy to decrease the total energy of the configuration.